The new director general of the BBC, George Entwistle, has been challenged to make the BBC "10 or 20%" better than it is despite having less money to do it on.

Formally unveiling Mark Thompson's successor, BBC Trust chairman Lord Patten described the new DG as a great creative leader who would build on the BBC's reputation as the greatest public service broadcaster and arguably the greatest broadcaster in the world.

But he added: "[The BBC] can and should be 10 or 20% better than it is."

Speaking just hours after the appointment culture secretary Jeremy Hunt said Entwistle must retain the corporation's "gold standard".

At a brief photo call outside the newly revamped Broadcasting House in central London, Patten said Entwistle was the unanimous choice of the BBC Trust.

Entwistle declined to take any questions from the press, making only a short statement in which he said he was privileged to be leading the greatest broadcasting organisation in the world.

He said his predecessor and friend Mark Thompson would be a tough act to follow.

Patten defended the £450,000 salary Entwistle would pick up, lower than Thompson's £617,000 but higher than some people had expected.

Patten said the salary was more than reasonable, and quipped to reporters: "I can't help it if you guessed it wrong."

He said Entwistle's salary was considerably less than some commercial television executives earned. "[It is a] reasonable salary for a public service job. More than reasonable," he said.

In a reference to the two defeated candidates – Ofcom director general Ed Richards and the corporation's chief operating officer, Caroline Thomson – Patten said it would have been possible to have a director general without a creative background, but said they would have had more credibility if they had.

Asked about Entwistle's perceived lack of commercial experience, Patten described him as a greatly respected cultural leader who was experienced in exploiting the BBC's programmes around the world.

He said that the challenge ahead, was to continue to improve the BBC's programmes at a time of financial restraint and retain the support of the public.

The culture secretary said George Entwistle's greatest challenge as incoming director general of the BBC is to weather the technological revolution while maintaining high standards.

Hunt, who was giving his first interview since giving evidence to the Leveson inquiry in May, also said: "The first [challenge] is how to make sure the BBC maintains its position as the gold standard for quality in British and global broadcasting, whilst managing the licence fee settlement which was a reasonable and fair settlement."

He added that the second challenge was steering the BBC through the "technological revolution" and that in two years the media industry would be in a "totally different place".

He praised Mark Thompson, the outgoing director general, for his handling of the BBC in a multi-platform era, adding that it would be a "huge challenge" to continue to adapt well to the changes.

Hunt also had warm words for Entwistle. He said: "There couldn't be someone with more experience of how the BBC works, with more diverse experience. I think he is someone who is hugely respected both inside and outside the organisation."

Entwistle will formally take over the reins at the BBC on 17 September, after Thompson has seen the corporation through the London Olympics.

Thompson said in a memo to staff following the appointment: "I've known George for many years and have watched one of the very best journalists and programme-makers of his generation become a formidable creative leader.

"He's someone who has the BBC's values running through his veins and a track record of backing talent and driving innovation with real conviction and courage. I believe he will be an outstanding DG and I want to wish him and all of you every success over the coming years."

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